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Treves F. — Topological Vector Spaces, Distributions And Kernels
Treves F. — Topological Vector Spaces, Distributions And Kernels

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Название: Topological Vector Spaces, Distributions And Kernels

Автор: Treves F.

Аннотация:

This text for upper-level undergraduates and graduate students
focuses on key notions and results in functional analysis. Extending
beyond the boundaries of Hilbert and Banach space theory, it explores
aspects of analysis relevant to the solution of partial differential
equations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 565

Добавлена в каталог: 19.09.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H^{s}$ Spaces      329
$L^{p}$-space      101
$L^{\infty}$-Space      105
$\epsilon$-norm      443
$\epsilon$-topology      429 434
$\mathfrak{C}^{k}$ topology      86
$\mathfrak{C}^{\infty}$ topology      89
$\mathfrak{S}$-topology      197 336
$\pi$-norm      443
$\pi$-topology      434
$\sigma$-algebra      549
$\sigma$-finite      99
Absolute value of measure      221
Absolute value of operator      490
Absolutely convergent series      459
Absolutely summable sequence      459
Absorbing      21
Accumulation point      51
Adjoint      252 488
Affine hyperplane      182
Algebraic dual      17
Algebraic transpose      17
Analytic functionals      231
Analytic functions      544
Antidual      116
Antilinear (also, semilinear)      116
Arzela's theorem      146
Ascoli's theorem      143
Baire closure      553
Baire space      74 553
Balanced      21
Banach space (also, B-space)      97
Banach — Steinhaus theorem      348
Barrel      58
Barreled      346
Basis of bounded sets      136
Basis of continuous seminorms      63
Basis of filter      7
Basis of neighborhoods      8
Bessel's inequality      121
Bidual      372
Bijection      18
Bilinear form      113
Bilinear map      420
Bipolar      362
Borel graph theorem      549
Borel set      549
Borel — Heine — Lebesgue theorem      51
Borel's theorem      390
Bounded set      136
Bounded set of distributions      359
Bracket of duality      227 238 425
Canonical LF-topology      132
Canonical map of TVS into algebraic dual of its dual      200
Canonical mapping onto quotient space      16
Carried (analytic functional carried by set)      237
Cauchy filter      37
Cauchy formula      90
Cauchy sequence      37
Cauchy — Riemann equations      90
Characteristic function      99 222
Closed convex hull      58
Closed graph theorem      168
Closed set      8
Closure      8
Codimension      81
Compact (also, completely continuous) map      483
Compact set, space      50
Comparison of filters      8
Comparison of topologies      9
Compatible, topology compatible with duality      369
Compatible, topology compatible with vector space structure      20
Complete set      38
Complete TVS      38
Completed tensor product      439
Completion      38 41
Completion of normed space      97
Complex conjugate measure      217
Compose of two mappings      17
Cone      192 195
Continuous function (or map)      11 12
Continuous linear form or functional      35
Continuous linear map      34
Continuous right inverse      543
Continuously differentiable functions      86
Convergent filter, sequence      10
Convex hull      57
Convex set      30 57
Convolution algebra      280
Convolution of analytic functionals      321
Convolution of distributions      293
Convolution of functions      278
Covering finer than another one      161
Cutting      302
d-convex      391
Definite positive form      60
Dense      9
density      217
Diagonal      535
Differentiable vector valued function      285
Differential operator      247
Differential polynomial      252
Differentiation monomial      251
Dimension of vector space      78
Dirac measure      217
Direct sum      81
Direct sum topology      515
Discrete topology      9
Distance      70
Distance to set      76
distribution      222
Distribution of finite order      258
Distribution with compact support      256
Distribution with support at origin      264
Dixmier — Schatten theorem      497
Dual      35
Dual of normed space      107
Dunford — Pettis theorem      471
Dvoretzky — Rogers theorem      467
Egoroff's theorem      103
Eigenspace      491
Eigenvalue      491
Entire function      152
Equicontinuous set of functions      142
Equicontinuous set of linear functions      142
Equismall at infinity      451
Equivalence relation      15
Equivalent modulo subspace      15
Equivalent norms      95
Equivalent seminorms      95
Essential supremum      105
Essentially bounded      105
Euclidean (also, Hermitian) norm      59
Exponential type (entire function of)      232
Extendable distribution      246
Extension (of distribution, of function)      246
Filter      6
Filter of neighborhoods      8
Filter of neighborhoods, of the origin      21
Filter, associated with sequence      7
Finer filter      8
Finer topology      9
Finest locally convex topology      134
Finite dimensional TVS      78
Finite dimensional vector space      19
Finite Taylor expansion      152
Fisher — Riesz theorem      102
Formal power series      25
Formal transpose of differential operator      249
Fourier series (also, Fourier expansion)      528
Fourier transformation of distributions      275
Fourier transformation of functions      268
Fourier — Borel (also, Fourier — Laplace) transform      237
Frechet space (also, F-space)      85
Fubini's theorem      416
Fundamental kernel      535
Gevrey class      160
Graph of linear map      167
Hahn — Banach theorem      181
Half-space      189
Hausdorff topology, space      31
Hausdorff TVS associated with given TVS      34
Heaviside function      276 297
Hermitian form      60 113
Hilbert norm      115
Hilbert space      115
Hilbert sum      121
Hoelder's inequality      205
Holomorphic function      89
Homeomorphism      51
Homomorphism      35 166
Hyperplane      81
Hypocontinuous      423
Hypoelliptic      535
Ideal      26
Image of filter      12
Image of map      16
Indicator of set      307
Inductive limit of locally convex spaces      515
Infinitely differentiable function      86
Infinitely dimensional vector space      78
Infracomplete      477
Initial topology      368
Injection of dual      243
Injective      17
Integrable function      101
Integrable step-function      99 468
Integral form      500
Integral map      503
Interior of set      8
Isometry      96 124
Isomorphism      35
Isomorphism of normed spaces      96 124
Isomorphism of pre-Hilbert spaces      124
K-Analytic space      556
Kernel distribution      509 532
Kernel of map      16
Kernel of seminorm      66
Kernels theorem      531
Laplace operator      324
Laplace transform      277
Lebesgue measure      99 217
Length of n-tuple      85
LF-Space      126
Line      82
Linear form, functional      17
Linear isometry      96 124
Linear map      15
Linear subvariety      15
Linearly disjoint      403
Locally compact TVS      81
Locally convex TVS      58
Locally finite covering      161
Locally integrable function      212 221
Mackey topology      369
Mackey's theorem      371
Maximum of absolute value      97
Meager set      553
Metric      70
Metrizable space, TVS      38 70
Minkowsky's inequality      99
Montel space      356
Montel's theorem      149
Multiplication of distribution by function      250
Multiplication of vector by scalar      14
Multiplicity of eigenvalue      491
Natural injection      16
Neighborhood of point      8
Nondegenerate form      113
Nonnegative form      60 114
Norm      59
Norm of functional, of map      107
Normable TVS      95
Normal space of distributions      302
Normed space      96
Normed space, associated with seminormed space      67
Nuclear map      478 479
Nuclear space      510
One-to-one map      15
Onto map      16
Open covering      161
Open mapping      166
Open mapping theorem      166
Open set      8
Order of differential operator      247 251
Order of differentiation      85
Order of distribution      258
Order relation (compatible with linear structure)      193
Orthogonal projection      118 120
Orthogonal to (or of) a set      119 121 196 241
Orthonormal basis      121
Orthonormal set      121
Osgood theorem      335
Paley — Wiener theorem      305
Parametrix      535
Parseval's identity, formula      122 271
Part (real or imaginary) of measure      217
Partition of unity      164
Periodic $\mathfrak{C}^{\infty}$ functions      528
Plancherel (also, Plancherel — Parseval) theorem      270
Pointed cone      193
polar      195
Polish space      549
Polydisk      90
Polynomials      129
Polynuclear      516
Positive definite      113
Positive linear functional      193
Positive measure      217
Positive operator      488
Positive square root of operator      489
Positively homogeneous      59
Pre-Hilbert space      60 114
Precompact      53
Preimage      11
Product of pre-Hilbert spaces      124
Product topology      13
Product vector space      18
Projection      83
Projective limit      29 514
Projective topology      434
Pseudofunctions      225
Quasicomplete      355
Quotient norm      97
Quotient normed space      97
Quotient seminorm      65
Quotient topology      33
Quotient TVS      33
Quotient vector space      15
Radon measure      211 216
Radon — Nicodym theorem      211
Rapidly decreasing at infinity distribution      315
Rapidly decreasing at infinity function      92
Rapidly decreasing sequence      527
Reflexive space      372
Regular kernel      536
Regularization      302
Regularizing kernel      533
Relatively compact      53
Restriction map      181
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